Device for Grinding Spinning Cots

ABSTRACT

The device has a rotating grinding surface and a receptacle into which a spinning cot to be ground is inserted. The receptacle is advanced in a direction toward the grinding surface until the spinning cot inserted into the receptacle contacts the grinding surface. A size determination device for determining the size of the spinning cot is provided, wherein the size determination device has distance sensors and a computing unit for deriving the size of the spinning cot. The distance sensors operate with measuring beams that have an orientation such that the measuring beams impinge on an outer peripheral surface of the spinning cot inserted into the receptacle on at least three points that are spaced apart from one another in a circumferential direction of the spinning cot.

BACKGROUND OF THE INVENTION

The invention concerns a device for grinding spinning cots, comprising:

-   -   a rotating grinding surface,     -   a receptacle into which the spinning cot to be ground is         insertable, means for advancing the receptacle in a direction         toward the grinding surface until contact is made between the         grinding surface and the spinning cot inserted into the         receptacle, and     -   a device for determining the size of the spinning cot inserted         into the receptacle, wherein this device is comprised of         detection means for at least one geometric value, wherein this         value is not the size of the spinning cot, and a computing unit         for deriving the size of the spinning cot based on a measured         geometric value detected by the detection means.

Such devices are used in connection with industrial processing of textile fibers. In spinning devices, the spinning cots perform the transport of the textile fibers. In this connection, the surfaces of the spinning cots that are usually made from plastic material are subject to great wear so that they must be frequently reground. The diameter of the spinning cots is sized from the start with oversize such that the cots can be reground several times by grinding devices configured for this purpose, wherein only a few tenths or hundredths of a millimeter are removed, respectively. After such a grinding treatment, the surface of the spinning cots is again exactly round and cylindrical.

For grinding a spinning cot, the spinning cot is fastened in the grinding machine on an automatically operating slide that advances the spinning cot by automatic control to the grinding surface of a grinding roller. Manipulation of the spinning cot to be reground is realized by means of a swivel arm that is provided with a receptacle for the axle of the spinning cot. The swivel arm with the spinning cot inserted therein is then advanced fully automatically against the grinding roller. For calculating the amount of removal the swivel arm is usually provided with an incremental encoder that detects the pivot angle and thus the movement of the swivel arm during the grinding process. For adjusting the zero point, the incremental point is detected that results upon pressing the cot against the grinding surface, i.e. upon first contact. Subsequently, the cot is ground wherein in practice two different methods are employed. According to the first method, all cots are ground to a predetermined diameter. According to a second method, they are all subjected to the same amount of removal and thus the same reduction of their diameter. The amount of removal is calculated based on the pivot angle difference that is detected by the incremental encoder. Since this is however an indirect measuring method, the measuring precision is determined by many influencing factors; in practice, this does not provide for a really precise calculation of the grinding result.

SUMMARY OF THE INVENTION

The invention has the object to provide a device for grinding spinning cots that enables a more exact measurement of the cot geometry and that operates moreover substantially free of influencing factors that falsify the measured result.

As a solution to the object a device having the aforementioned features is proposed that is characterized by distance sensors operating with measuring beams and having an orientation such that the measuring beams impinge on the outer peripheral surface of a spinning cot inserted into a receptacle at least on three points that are spaced apart from one another in the circumferential direction of the spinning cot.

Such a device enables a direct measurement of the geometry of the respectively inserted spinning cot, i.e., of its diameter or radius. The device according to the invention operates therefore substantially free of influencing factors that falsify the measured result. By a direct detection of the surface of the respective spinning cot, the operation of the measuring unit is relatively insensitive with regard to possible dust deposits. Also, the hardness and the flexibility of the material of the cots to be ground and the state of their axles have hardly any effect on the measured result. A contribution to precision is moreover provided by the fact that the measuring system works completely contactless.

According to a preferred embodiment, the distance sensors operate with an orientation such that all measuring beams impinge on the outer peripheral surface of the spinning cots inserted into the receptacle at the same axial length of the spinning cot. In this way, measurement imprecisions are excluded that can occur in case of a slight axial displacement of the measuring beams.

A further embodiment is characterized by an orientation of the measuring beams such that at least one first measuring beam is directed to a point adjacent to the center axis of the spinning cot, and at least one additional measuring beam is also directed to a point adjacent to the center axis but onto the side facing away from the first measuring beam. This enables even more precise measured results.

According to one constructive embodiment of the device, the distance sensors are fastened to a common holder; this enables a very precise positioning of the sensors and thus an improvement of the measuring precision. Preferably, the holder is provided with positive locking elements onto which or in which the distance sensors are mounted. Additionally, a screw connection with the holder can be provided.

In another embodiment it is proposed that the distance sensors are rigidly connected to the receptacle, preferably embodied as a swivel arm, or the holder is rigidly connected to the receptacle. This enables measurement at any time during the inward and outward pivoting of the swivel arms because even then the spinning cot is within the detection range of the distance sensors. Already at the time of setting up or preparing the actual grinding process, a detection of the actual state of the spinning cot is possible. Under no circumstances is it possible that a play possibly present at the swivel arm can have an effect on the obtained measured result.

BRIEF DESCRIPTION OF THE DRAWINGS

One embodiment of the invention will be explained in the following with the aid of the drawings. It is shown in:

FIG. 1 a side view of the grinding machine with a spinning cot to be ground inserted therein;

FIG. 2 a schematic illustration of the basic configuration and of the function of a laser distance sensor operating according to the principle of triangulation;

FIG. 3 a schematic illustration of the arrangement of a total of three laser distance sensors relative to the spinning cot to be ground;

FIG. 4 in a perspective illustration the attachment of three distance sensors on a holder plate;

FIG. 5 an illustration comparable to FIG. 3 for explaining the geometric conditions for a radius determination by means of three points; and

FIG. 6 a further illustration for deriving the geometric conditions.

DESCRIPTION OF PREFERRED EMBODIMENTS

In FIG. 1 a part of a grinding machine for grinding spinning cots is shown in a greatly simplified illustration. Such grinding machines are utilized primarily in spinning works. In spinning works the spinning cots function as transport rollers for guiding the textile fibers; in this connection, the cots are subject to great wear so that frequent regrinding is required. From the start, the diameter of the spinning cot is oversized so that they can be reground several times.

FIG. 1 shows for this purpose a frame 1 of the grinding machine with a grinding roller 2 that is also arranged on the frame 1 and is driven by a drive motor. The outer peripheral surface of this grinding roller 2 provides the grinding surface 3 for grinding the spinning cot referenced in the drawings by reference numeral 5. For grinding the spinning cot 5, a slide 7 is arranged on the frame 1 so as to be horizontally movable, i.e. essentially movable in the direction toward the grinding roller 2. On the slide 7 a swivel arm 9 is supported at 8. On the end of the swivel arm facing the grinding roller 2, the swivel arm 9 has a receptacle 10 for the axle of the spinning cot 5. By actuating the swivel arm 9 as a result of the force F, the swivel arm 9 pivots together with the inserted spinning cot 5 downwardly so that the spinning cot 5 comes to rest against a driven drive roller 12 arranged underneath. As a result of friction the drive roller 12 rotates the spinning cot 5 so that the cot during the grinding process is rotated counter to the rotational direction of the grinding roller 2 and its surface is ground by being in contact with the grinding surface 3 of the grinding roller 2.

On the swivel arm 9 a holder 13 is fastened and on it, in turn, three distance sensors 15 a, 15 b, 15 c are fastened. The measuring beams 17 a, 17 b and 17 c of these distance sensors 15 a, 15 b, 15 c are oriented toward the surface, i.e., the outer peripheral surface 18, of the spinning cot 5 to be ground on the grinding machine.

The distance sensors 15 a, 15 b, 15 c are parts of a device for determining, i.e., calculating, the size of the spinning cot 5. This device is comprised of the distance sensors as well as a computing unit 19 connected to the signal outputs 16 of the distance sensors 15 a, 15 b, 15 c. In the computing unit 19 the diameter of the spinning cot 5 is derived based on the three geometric values acquired by the three distance sensors. At the same time, the computing unit 19 controls the drive 20 of the slide 7 and optionally the pressing force F pressing on the swivel arm 9 so that it controls in this way the grinding process.

Details of the function of the distance sensors 15 a, 15 b, 15 c will be explained in the following with the aid of FIG. 2. Each distance sensor is a laser distance sensor whose distance measurement is based on the principle of triangulation. A laser beam 22 that is emitted by the distance sensor impinges as a small dot on the object. The receiver 23 of the laser distance sensors detects the position of this dot by angle detection. The sensor measures principally this angle α and calculates then the distance D to the point of impingement. In FIG. 2 it is also illustrated how the possible resolution and precision of the distance sensors changes with the distance. The same distance causes in the vicinity of the sensor a large angle change and farther away a much smaller angle change. By means of a processor, this non-linear behavior is corrected so that the output signal 16 is linear relative to the distance. D1 refers to the distance range in which the distance sensor works optimally; the distance range D2 should be avoided. The receiver 23 in the interior of the distance sensor is configured as a linear photo diode array. The photo diode array is read out by an incorporated micro controller. Based on the light distribution on the photo diode array the controller calculates exactly the angle α and, based thereon, it calculates the distance D to the spinning cot. This distance is either transmitted to a serial port or converted into an output current that is proportional to the distance D. By combining a photo diode array and a micro controller, disruptive reflections can be suppressed and, in this way, reliable data can be obtained even for a critical surface of the spinning cot.

In FIG. 3 the geometric arrangement of the three distance sensors 15 a, 15 b, 15 c relative to the spinning cot 5 to be measured is illustrated. Since the center axis of the spinning cot that has partially a greater or a smaller diameter is variable, a measurement by means of at least three points is required for the determination of the actual diameter of the spinning cot. Therefore, at least three distance sensors 15 a, 15 b, 15 c are required. FIG. 3 also shows that the first measuring beam 17 a is oriented to a point spaced from the center axis 24 of the spinning cot at a spacing a1. The third measuring beam 17 c is also oriented to a point spaced from the center axis 24 at a spacing a2 but at the side facing away from the first measuring beam 17 a. The central one 15 b of the distance sensors is arranged such that its measuring beam 17 b images on the center axis 24 of the spinning cot 5 not far from the center axis 24. In this way, larger spacings a1 and a2 of the measuring beams 17 a and 17 c and a smaller spacing of the measuring beams 17 b relative to the center axis 24 result. All three measuring beams impinge, viewed in the circumferential direction, at a spacing to one another on the surface of the spinning cot 5.

In FIG. 4 the arrangement of the distance sensors on the common holder 13 is shown. The holder 13 is a plate provided with three grooves 26 a, 26 b, 26 c. Into these grooves, the receptacles for the distance sensors, already screwed to the sensors, are inserted so that the distance sensors are seated positive lockingly in the holder 13. This enables a positioning of the three distance sensors relative to one another such that they are positioned very closely to one another and very precisely relative to one another, wherein their measuring beams are not aligned parallel to one another. Additionally, a screw connection of the distance sensors and the holder 13 is provided.

In the illustrated embodiment the holder 13, as shown especially in FIG. 1, is connected to the swivel arm 9. It is also possible that the holder 13 is stationarily fastened on the frame 1 wherein in this case the orientation of the sensors must be such that the measuring beams are directed onto three different points of the outer peripheral surface 18 of the spinning cot 5. It is possible to clean the distance sensors and the spinning cot by means of a compressed air jet generated by a compressed air device.

In the following the radii/diameter determination by means of three points will be explained, including the mathematical derivation.

First the coordinate points must be set which will be explained in the following with the aid of FIG. 5. The zero point of the coordinates can be freely positioned e.g. horizontally aligned with the point 2 (horizontal spacing P2=0) and vertically 10 mm under the lowest laser point (vertical spacing P1=10). In order to obtain a more precise measured result, the exact horizontal and vertical spacings must be determined. For this purpose the laser distance sensors must be aligned exactly. Their horizontal and vertical spacings relative to one another must be determined. They are determined with the aid of a standardized part, e.g. a plug limit gauge, as well with the aid of the measured distances of the sensor to the standardized part. In this way, the measuring system can be calibrated and is thus insensitive relative to mounting tolerances. For the three laser distance sensors (in the following for short “laser”) the following coordinates will result (FIG. 5):

Laser P1: x ₁=measured value P1*sin 70°+horizontal spacing P1 y ₁=measured value P1*cos 70°+vertical spacing P1

Laser P2: x₂=measured value P2 y₂=vertical spacing P2

Laser P3: x ₃=measured value P3*sin 70°+horizontal spacing P3 y ₃=vertical spacing P3−cos 70°*measured value P3

Based on the three determined reference points P₁(x₁|y₁), P₂(x₂|y₂), P₃(x₃|y₃) on a circle, it is possible to determine by means of the general circle equation a closed equation for the radius of this circle (with the center M₁(x_(m)|y_(m))) in the following way:

All three predetermined points have relative to the center r by definition the same spacing r (the radius of the circle) that can be determined by means of the Pythagorean theorem: r ²=(x ₁ −x _(m))²+(y ₁ −y ₁ −y _(m))²  I: r ²=(x ₂ −x _(m))²+(y ₂ −y _(m))²  II: r ²=(x ₃ −x _(m))²+(y ₃ −y _(m))²  III: (x ₁ −x _(m))²+(y ₁ −y _(m))²=(x ₂ −x _(m))²+(y ₂ −y _(m))²  IV (I equated to II): r ²=(x ₂ −x _(m))²+(y ₂ −y _(m))²=(x ₃ −x _(m))²+(y ₃ −y _(m))²  V (II equated to III): (x ₁ −x _(m))²+(y ₁ −y _(m))²=(x ₂ −x _(m))²+(y ₂ −y _(m))² ⇄ (x ₁ ²−2x ₁ x _(m) +x _(m) ²)+(y ₁ ²−2y ₁ y _(m) +y _(m) ²)=(x ₂ ²−2x ₂ x _(m) +x _(m) ²)+(y ₂ ²−2y ₂ y _(m) +y _(m) ²) ⇄ x ₁ ²−2x ₁ x _(m) +x _(m) ² +y ₁ ²−2y ₁ y _(m) +y _(m) ² =x ₂ ²−2x ₂ x _(m) +x _(m) ² +y ₂ ²−2y ₂ y _(m) +y _(m) ² ⇄ −2x ₁ x _(m) +x _(m) ²−(−2x ₂ x _(m) +x _(m) ²)=x ₂ ² +y ₂ ²−2y ₂ y _(m) +y _(m) ²−(x ₁ ²−2y ₁ y _(m) +y _(m) ²) ⇄ −2x ₁ x _(m) +x _(m) ²+2x ₂ x _(m) −x _(m) ² =x ₂ ² +y ₂ ²−2y ₂ y _(m) +y _(m) ² −x ₁ ² −y ₁ ²+2y ₁ y _(m) −y _(m) ² ⇄ −2x ₁ x _(m)+2x ₂ x _(m) =x ₂ ² +y ₂ ²−2y ₂ y _(m) −x ₁ ² −y ₁ ²+2y ₁ y _(m) ⇄ (−2x ₁+2x ₂)·x _(m) =x ₂ ² y ₂ ² −x ₁ ² −y ₁ ²+(2y ₁−2y ₂)·y _(m)  VI (based on IV, for x_(m) the following results): ⇄ $x_{m} = \frac{x_{2}^{2} + y_{2}^{2} - x_{1}^{2} - y_{1}^{2} + {\left( {{2y_{1}} - {2y_{2}}} \right) \cdot y_{m}}}{{{- 2}x_{1}} + {2x_{2}}}$

VII (in analogy, based on V the following results for x_(m)): $x_{m} = \frac{x_{3}^{2} + y_{3}^{2} - x_{2}^{2} - y_{2}^{2} + {\left( {{2y_{2}} - {2y_{3}}} \right) \cdot y_{m}}}{{{- 2}x_{2}} + {2x_{3}}}$

VIII (when VI and VII are equated, the following results): $\frac{x_{2}^{2} + y_{2}^{2} - x_{1}^{2} - y_{1}^{2} + {\left( {{2y_{1}} - {2y_{2}}} \right) \cdot y_{m}}}{{{- 2}x_{1}} + {2x_{2}}} = {\left. \frac{\begin{matrix} {x_{3}^{2} + y_{3}^{2} - x_{2}^{2} - y_{2}^{2} +} \\ {\left( {{2y_{2}} - {2y_{3}}} \right) \cdot y_{m}} \end{matrix}}{{{- 2}x_{2}} + {2x_{3}}}\Leftrightarrow{\frac{x_{2}^{2} + y_{2}^{2} - x_{1}^{2} - y_{1}^{2}}{{{- 2}x_{1}} + {2x_{2}}} + {\frac{{2y_{1}} - {2y_{2}}}{{{- 2}x_{1}} + {2x_{2}}} \cdot y_{m}}} \right. = {\left. {\frac{x_{3}^{2} + y_{3}^{2} - x_{2}^{2} - y_{2}^{2}}{{{- 2}x_{2}} + {2x_{3}}} + {\frac{{2y_{2}} - {2y_{3}}}{{{- 2}x_{2}} + {2x_{3}}} \cdot y_{m}}}\Leftrightarrow{\frac{x_{2}^{2} - x_{1}^{2} + y_{2}^{2} - y_{1}^{2}}{2\left( {x_{2} - x_{1}} \right)} + {\frac{y_{1} - y_{2}}{x_{2} - x_{1}} \cdot y_{m}}} \right. = {\frac{x_{3}^{2} - x_{2}^{2} + y_{3}^{2} - y_{2}^{2}}{2\left( {x_{3} - x_{2}} \right)} + {\frac{y_{2} - y_{3}}{x_{3} - x_{2}} \cdot y_{m}}}}}$ ⇄(3. Binomial Equation) ${\frac{{\left( {x_{2} + x_{1\quad}} \right)\left( {x_{2} - x_{1}} \right)} + y_{2}^{2} - y_{1}^{2}}{2\left( {x_{2} - x_{1}} \right)} + {\frac{y_{1} - y_{2}}{x_{2} - x_{1}} \cdot y_{m}}} = {\left. {\frac{{\left( {x_{3} + x_{2\quad}} \right)\left( {x_{3} - x_{2}} \right)} + y_{3}^{2} - y_{2}^{2}}{2\left( {x_{3} - x_{2}} \right)} + {\frac{y_{2} - y_{3}}{x_{3} - x_{2}} \cdot y_{m}}}\Leftrightarrow{\frac{\left( {x_{2} + x_{1}} \right)}{2} + \frac{y_{2}^{2} - y_{1}^{2}}{2\left( {x_{2} - x_{1}} \right)} + {\frac{y_{1} - y_{2}}{x_{2} - x_{1}} \cdot y_{m}}} \right. = {\left. {\frac{\left( {x_{3} + x_{2}} \right)}{2} + \frac{y_{3}^{2} - y_{2}^{2}}{2\left( {x_{3} - x_{2}} \right)} + {\frac{y_{2} - y_{3}}{x_{3} - x_{2}} \cdot y_{m}}}\Leftrightarrow{\frac{\left( {x_{2} + x_{1}} \right)}{2} + \frac{y_{2}^{2} - y_{1}^{2}}{2\left( {x_{2} - x_{1}} \right)} - \left( {\frac{\left( {x_{3} + x_{2}} \right)}{2} + \frac{y_{3}^{2} - y_{2}^{2}}{2\left( {x_{3} - x_{2}} \right)}} \right)} \right. = {\left. {\left( {\frac{y_{2} - y_{3}}{x_{3} - x_{2}} - \frac{y_{1} - y_{2}}{x_{2} - x_{1}}} \right) \cdot y_{m}}\Leftrightarrow{\frac{\left( {x_{2} + x_{1}} \right)}{2} + \frac{y_{2}^{2} - y_{1}^{2}}{2\left( {x_{2} - x_{1}} \right)} - \frac{\left( {x_{3} + x_{2}} \right)}{2} - \frac{y_{3}^{2} - y_{2}^{2}}{2\left( {x_{3} - x_{2}} \right)}} \right. = {\left. {\left( {\frac{y_{2} - y_{3}}{x_{3} - x_{2}} - \frac{y_{1} - y_{2}}{x_{2} - x_{1}}} \right) \cdot y_{m}}\Leftrightarrow\frac{\frac{\left( {x_{2} + x_{1}} \right)}{2} + \frac{y_{2}^{2} - y_{1}^{2}}{2\left( {x_{2} - x_{1}} \right)} - \frac{\left( {x_{3} + x_{2}} \right)}{2} - \frac{y_{3}^{2} - y_{2}^{2}}{2\left( {x_{3} - x_{2}} \right)}}{\left( {\frac{y_{2} - y_{3}}{x_{3} - x_{2}} - \frac{y_{1} - y_{2}}{x_{2} - x_{1}}} \right)} \right. = y_{m}}}}}$ $y_{m} = \frac{x_{1} - x_{3} + \frac{y_{2}^{2} - y_{1}^{2}}{x_{2} - x_{1}} - \frac{y_{3}^{2} - y_{2}^{2}}{x_{3} - x_{2}}}{2 \cdot \left( {\frac{y_{2} - y_{3}}{x_{3} - x_{2}} - \frac{y_{1} - y_{2}}{x_{2} - x_{1}}} \right)}$

IX (when, based on IV and V, y_(m) is calculated and not x_(m) respectively, the following results in analogy): $y_{m} = \frac{x_{2}^{2} + y_{2}^{2} - x_{1}^{2} - y_{1}^{2} + {\left( {{2x_{1}} - {2x_{2}}} \right) \cdot x_{m}}}{{{- 2}y_{1}} + {2y_{2\quad}}}$ $y_{m} = \frac{x_{3}^{2} + y_{3}^{2} - x_{2}^{2} - y_{2}^{2} + {\left( {{2x_{2}} - {2x_{3}}} \right) \cdot x_{m}}}{{{- 2}y_{2}} + {2y_{3}}}$

X (when they are equated (as VI and VII above), it follows in analogy): $x_{m} = \frac{\frac{x_{2}^{2} - x_{1}^{2}}{y_{2} - y_{1}} - \frac{x_{3}^{2} - x_{2}^{2}}{y_{3} - y_{2}} + y_{1} - y_{3}}{2\left( {\frac{x_{2} - x_{3}}{y_{3} - y_{2}} - \frac{x_{1} - x_{2}}{y_{2} - y_{1}}} \right)}$

XI (a closed equation for r results when x_(m) and y_(m) are used in I (or alternatively II or III): $r = \sqrt{\left( {x_{1} - \frac{\frac{x_{2}^{2} - x_{1}^{2}}{y_{2} - y_{1}} - \frac{x_{3}^{2} - x_{2}^{2}}{y_{3} - y_{2}} + y_{1} - y_{3}}{2\left( {\frac{x_{2} - x_{3}}{y_{3} - y_{2}} - \frac{x_{1} - x_{2}}{y_{2} - y_{1}}} \right)}} \right)^{2} + \left( {y_{1} - \frac{x_{1} - x_{3} + \frac{y_{2}^{2} - y_{1}^{2}}{x_{2} - x_{1}} - \frac{y_{3}^{2} - y_{2}^{2}}{x_{3} - x_{2}}}{2 \cdot \left( {\frac{y_{2} - y_{3}}{x_{3} - x_{2}} - \frac{y_{1} - y_{2}}{x_{2} - x_{1}}} \right)}} \right)^{2}}$

Alternatively, a geometric approach is possible. In this case, the points P₁, P₂ and P₃ are considered to be the corners of a triangle.

From geometry it is known that:

The perpendicular bisectors of a side of a triangle intersect at the center of the circumcircle of the triangle. The circumcircle of the triangle is exactly the circle on which all three corners are located.

It is thus sufficient to determine the point of intersection of two such perpendicular bisectors in order to determine the center of the circle on which P₁, P₂ and P₃ are positioned.

In the following, the perpendicular bisectors A (on the line S₁= P₁P₂ ) and B (on the line S₂= P₂P₃ ) are calculated.

The perpendicular bisectors are straight lines. Each straight line is defined when one point on this straight line and its gradient are known.

The perpendicular bisectors A and B are positioned exactly on the center of the lines S₁ and S₂ and thus on the following coordinates: ${x_{A} = \frac{x_{1} + x_{2}}{2}};{y_{A} = {{\frac{y_{1} + y_{2}}{2}\quad{and}\quad x_{B}} = \frac{x_{2} + x_{3}}{2}}};{y_{B} = \frac{y_{2} + y_{3}}{2}}$

Accordingly, for both perpendicular bisectors A and B the coordinates of one point each are already known.

The gradient of a straight line or a line results from Δy/Δx (that is: ,,height difference per width difference”).

For the lines S₁ and S₂ this is $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\quad{and}\quad{\frac{y_{3} - y_{2}}{x_{3} - x_{2}}.}$

The gradient of a perpendicular line (thus also of the two perpendicular bisectors of the side A and B to be determined) result always as the negative reciprocal value of the gradient of the straight line that is the origin so that the following applies: $m_{A} = {{{- \frac{x_{2} - x_{1}}{y_{2} - y_{1}}}\quad{and}\quad m_{B}} = {- \frac{x_{3} - x_{2}}{y_{3} - y_{2}}}}$

For straight lines there is a so-called “standard form”: G(x)=mx+b

For the perpendicular bisectors A and B, m_(A) and m_(B) are already available from the last calculation.

The so-called ,,y-axis section” b results from the gradient m and the coordinates of a point x_(p) and y_(p) by the following equation: b=y _(p) −m·x _(p), thus for A and B: b _(A) =y _(A) −m _(A) ·x _(A) and b _(B) =y _(B) −m _(B) ·x _(B)

From functional analysis it is known that:

The x-coordinate of the point of intersection of the perpendicular bisectors A and B is at: $x_{m} = \frac{b_{B} - b_{A}}{m_{A} - m_{B}}$

The y-coordinate of the point of intersection thus is: y _(m) =m _(A) ·x _(m) +b _(A)

The radius of the circle then is: r=√{square root over ((x ₁ −x _(m))²+(y ₁ −y _(m))²)}.

The specification incorporates by reference the entire disclosure of German priority document 10 2005 035 581.1 having a filing date of Jul. 29, 2005.

While specific embodiments of the invention have been shown and described in detail to illustrate the inventive principles, it will be understood that the invention may be embodied otherwise without departing from such principles. 

1. A device for grinding spinning cots, the device comprising: a rotating grinding surface; a receptacle into which the spinning cot to be ground is insertable; means for advancing the receptacle in a direction toward the grinding surface until the spinning cot inserted into the receptacle contacts the grinding surface; a size determination device for determining a size of the spinning cot inserted into the receptacle, wherein the size determination device comprises distance sensors and a computing unit for deriving the size of the spinning cot based on at least one geometric value acquired by the distance sensors; wherein the distance sensors operate with measuring beams that have an orientation such that the measuring beams impinge on at least a first point, a second point, and a third point of an outer peripheral surface of the spinning cot inserted into the receptacle, wherein the first, second, and third points are spaced apart from one another in a circumferential direction of the spinning cot.
 2. The device according to claim 1, wherein the orientation of the measuring beams is such that all of the measuring beams impinge at a same axial length of the spinning cot on the outer peripheral surface of the spinning cot.
 3. The device according to claim 1, wherein the orientation of the measuring beams is such that at least a first one of the measuring beams is directed to the first point that is adjacent to a center axis of the spinning cot and at least a second one of the measuring beams is directed to the second point that is also adjacent to the center axis but on a side facing away from the first one of the measuring beams.
 4. The device according to claim 3, wherein the measuring beams are not parallel to one another.
 5. The device according to claim 1, further comprising a common holder, wherein the distance sensors are fastened to the common holder.
 6. The device according to claim 5, wherein the common holder has positive locking elements on which or in which the distance sensors are mounted.
 7. The device according to claim 6, wherein the distance sensors are additionally screwed onto the common holder.
 8. The device according to claim 6, wherein the common holder is rigidly connected to the receptacle.
 9. The device according to claim 1, wherein the distance sensors are rigidly connected to the receptacle.
 10. The device according to claim 1, wherein the distance sensors operate by triangulation.
 11. The device according to claim 10, wherein the distance sensors are laser distance sensors.
 12. The device according to claim 1, comprising a compressed air device for cleaning the distance sensors and the spinning cot. 